Abstract

This paper presents a method to improve the dynamic range of white light interferometer (WLI) based polarization mode coupling (PMC) measurement system beyond 100 dB. The limitation of interference beat noise is overcame by analyzing in detail the inherent noises that have impacts on the detection sensitivity. An improved PMC measurement system and method are proposed for testing ultra-high polarization extinction ratio (PER) of polarization-related devices. The method can improve dynamic range dramatically through eliminating interference beat noise and enhancing the tested interference intensity simultaneously, which are verified theoretically and experimentally. In addition, a Y-junction with ~80 dB PER of LiNbO3 chip corresponding to a weak signal is tested as an application example. The results demonstrate that the high PER interferogram can be identified clearly and steadily with standard deviation 0.9 dB (3σ) @ ~80 dB. This proposed method is highly beneficial in fabrication and evaluation for polarization devices with ultra-high PER.

© 2016 Optical Society of America

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2016 (1)

2015 (4)

2014 (2)

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014).
[Crossref] [PubMed]

2013 (1)

S. H. Hsu, C. Y. Tsou, M. S. Hsieh, and C. Y. Lin, “Low-coherence interferometric fiber sensor with improved resolution using stepper motor assisted optical ruler,” Opt. Fiber Technol. 19(3), 223–226 (2013).
[Crossref]

2012 (1)

2011 (1)

2008 (1)

2007 (1)

2002 (1)

2000 (1)

1999 (1)

1993 (2)

K. Takada, T. Kitagawa, M. Shimizu, and M. Horiguchi, “High-sensitivity low coherence reflectometer using erbium-doped superfluorescent fibre source and erbium-doped power amplifier,” Electron. Lett. 29(4), 365–367 (1993).
[Crossref]

Y. J. Rao, Y. N. Ning, and D. A. Jackson, “Synthesized source for white-light sensing systems,” Opt. Lett. 18(6), 462–464 (1993).
[Crossref] [PubMed]

1992 (1)

W. V. Sorin and D. M. Baney, “A simple intensity noise reduction technique for optical low-coherence reflectometry,” IEEE Photonics Technol. Lett. 4(12), 1404–1406 (1992).
[Crossref]

1991 (1)

K. Takada, A. Himeno, and K. Yukimatsu, “Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry,” Appl. Phys. Lett. 59(20), 2483–2485 (1991).
[Crossref]

1987 (1)

1986 (2)

K. Takada, J. Noda, and K. Okamoto, “Measurement of spatial distribution of mode coupling in birefringent polarization-maintaining fiber with new detection scheme,” Opt. Lett. 11(10), 680–682 (1986).
[Crossref] [PubMed]

I. Yokohama, K. Okamoto, and J. Noda, “Analysis of fiber-optic polarizing beam splitters consisting of fused-taper couplers,” J. Lightwave Technol. 4(9), 1352–1359 (1986).
[Crossref]

Baney, D. M.

W. V. Sorin and D. M. Baney, “A simple intensity noise reduction technique for optical low-coherence reflectometry,” IEEE Photonics Technol. Lett. 4(12), 1404–1406 (1992).
[Crossref]

Bao, X.

Cai, J.

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Chai, J.

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

Chen, H.

Chen, L.

Chen, X.

Chida, K.

Dong, Y.

Fan, X.

Green, W. M. J.

Guo, Z.

He, Z.

Himeno, A.

K. Takada, A. Himeno, and K. Yukimatsu, “Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry,” Appl. Phys. Lett. 59(20), 2483–2485 (1991).
[Crossref]

Horiguchi, M.

K. Takada, T. Kitagawa, M. Shimizu, and M. Horiguchi, “High-sensitivity low coherence reflectometer using erbium-doped superfluorescent fibre source and erbium-doped power amplifier,” Electron. Lett. 29(4), 365–367 (1993).
[Crossref]

Hou, L.

Z. Yu, J. Yang, Y. Yuan, C. Li, S. Liang, L. Hou, F. Peng, B. Wu, J. Zhang, Z. Liu, and L. Yuan, “Quasi-distributed birefringence dispersion measurement for polarization maintain device with high accuracy based on white light interferometry,” Opt. Express 24(2), 1587–1597 (2016).
[Crossref] [PubMed]

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

Hsieh, M. S.

S. H. Hsu, C. Y. Tsou, M. S. Hsieh, and C. Y. Lin, “Low-coherence interferometric fiber sensor with improved resolution using stepper motor assisted optical ruler,” Opt. Fiber Technol. 19(3), 223–226 (2013).
[Crossref]

Hsu, S. H.

S. H. Hsu, C. Y. Tsou, M. S. Hsieh, and C. Y. Lin, “Low-coherence interferometric fiber sensor with improved resolution using stepper motor assisted optical ruler,” Opt. Fiber Technol. 19(3), 223–226 (2013).
[Crossref]

Huang, S.

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Izatt, J. A.

Jackson, D. A.

Jia, D.

Jin, W.

Jing, W.

Kitagawa, T.

K. Takada, T. Kitagawa, M. Shimizu, and M. Horiguchi, “High-sensitivity low coherence reflectometer using erbium-doped superfluorescent fibre source and erbium-doped power amplifier,” Electron. Lett. 29(4), 365–367 (1993).
[Crossref]

Li, C.

Z. Yu, J. Yang, Y. Yuan, C. Li, S. Liang, L. Hou, F. Peng, B. Wu, J. Zhang, Z. Liu, and L. Yuan, “Quasi-distributed birefringence dispersion measurement for polarization maintain device with high accuracy based on white light interferometry,” Opt. Express 24(2), 1587–1597 (2016).
[Crossref] [PubMed]

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Li, Z.

Liang, S.

Z. Yu, J. Yang, Y. Yuan, C. Li, S. Liang, L. Hou, F. Peng, B. Wu, J. Zhang, Z. Liu, and L. Yuan, “Quasi-distributed birefringence dispersion measurement for polarization maintain device with high accuracy based on white light interferometry,” Opt. Express 24(2), 1587–1597 (2016).
[Crossref] [PubMed]

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

Lin, C. Y.

S. H. Hsu, C. Y. Tsou, M. S. Hsieh, and C. Y. Lin, “Low-coherence interferometric fiber sensor with improved resolution using stepper motor assisted optical ruler,” Opt. Fiber Technol. 19(3), 223–226 (2013).
[Crossref]

Liu, Q.

Liu, T.

Liu, Z.

Z. Yu, J. Yang, Y. Yuan, C. Li, S. Liang, L. Hou, F. Peng, B. Wu, J. Zhang, Z. Liu, and L. Yuan, “Quasi-distributed birefringence dispersion measurement for polarization maintain device with high accuracy based on white light interferometry,” Opt. Express 24(2), 1587–1597 (2016).
[Crossref] [PubMed]

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Lu, Z.

Man, X.

Meng, Z.

Ning, Y. N.

Noda, J.

Okamoto, K.

I. Yokohama, K. Okamoto, and J. Noda, “Analysis of fiber-optic polarizing beam splitters consisting of fused-taper couplers,” J. Lightwave Technol. 4(9), 1352–1359 (1986).
[Crossref]

K. Takada, J. Noda, and K. Okamoto, “Measurement of spatial distribution of mode coupling in birefringent polarization-maintaining fiber with new detection scheme,” Opt. Lett. 11(10), 680–682 (1986).
[Crossref] [PubMed]

Peng, F.

Z. Yu, J. Yang, Y. Yuan, C. Li, S. Liang, L. Hou, F. Peng, B. Wu, J. Zhang, Z. Liu, and L. Yuan, “Quasi-distributed birefringence dispersion measurement for polarization maintain device with high accuracy based on white light interferometry,” Opt. Express 24(2), 1587–1597 (2016).
[Crossref] [PubMed]

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Rao, Y. J.

Rollins, A. M.

Rooks, M. J.

Sekaric, L.

Shimizu, M.

K. Takada, T. Kitagawa, M. Shimizu, and M. Horiguchi, “High-sensitivity low coherence reflectometer using erbium-doped superfluorescent fibre source and erbium-doped power amplifier,” Electron. Lett. 29(4), 365–367 (1993).
[Crossref]

Song, D.

Sorin, W. V.

W. V. Sorin and D. M. Baney, “A simple intensity noise reduction technique for optical low-coherence reflectometry,” IEEE Photonics Technol. Lett. 4(12), 1404–1406 (1992).
[Crossref]

Takada, K.

K. Takada, T. Kitagawa, M. Shimizu, and M. Horiguchi, “High-sensitivity low coherence reflectometer using erbium-doped superfluorescent fibre source and erbium-doped power amplifier,” Electron. Lett. 29(4), 365–367 (1993).
[Crossref]

K. Takada, A. Himeno, and K. Yukimatsu, “Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry,” Appl. Phys. Lett. 59(20), 2483–2485 (1991).
[Crossref]

K. Takada, K. Chida, and J. Noda, “Precise method for angular alignment of birefringent fibers based on an interferometric technique with a broadband source,” Appl. Opt. 26(15), 2979–2987 (1987).
[Crossref] [PubMed]

K. Takada, J. Noda, and K. Okamoto, “Measurement of spatial distribution of mode coupling in birefringent polarization-maintaining fiber with new detection scheme,” Opt. Lett. 11(10), 680–682 (1986).
[Crossref] [PubMed]

Tsou, C. Y.

S. H. Hsu, C. Y. Tsou, M. S. Hsieh, and C. Y. Lin, “Low-coherence interferometric fiber sensor with improved resolution using stepper motor assisted optical ruler,” Opt. Fiber Technol. 19(3), 223–226 (2013).
[Crossref]

Vlasov, Y. A.

Wang, S.

Wang, Z.

Wu, B.

Z. Yu, J. Yang, Y. Yuan, C. Li, S. Liang, L. Hou, F. Peng, B. Wu, J. Zhang, Z. Liu, and L. Yuan, “Quasi-distributed birefringence dispersion measurement for polarization maintain device with high accuracy based on white light interferometry,” Opt. Express 24(2), 1587–1597 (2016).
[Crossref] [PubMed]

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Xu, P.

Yan, D.

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Yang, J.

Z. Yu, J. Yang, Y. Yuan, C. Li, S. Liang, L. Hou, F. Peng, B. Wu, J. Zhang, Z. Liu, and L. Yuan, “Quasi-distributed birefringence dispersion measurement for polarization maintain device with high accuracy based on white light interferometry,” Opt. Express 24(2), 1587–1597 (2016).
[Crossref] [PubMed]

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Yao, X.

Ye, W.

Yokohama, I.

I. Yokohama, K. Okamoto, and J. Noda, “Analysis of fiber-optic polarizing beam splitters consisting of fused-taper couplers,” J. Lightwave Technol. 4(9), 1352–1359 (1986).
[Crossref]

Yu, Z.

Yuan, L.

Z. Yu, J. Yang, Y. Yuan, C. Li, S. Liang, L. Hou, F. Peng, B. Wu, J. Zhang, Z. Liu, and L. Yuan, “Quasi-distributed birefringence dispersion measurement for polarization maintain device with high accuracy based on white light interferometry,” Opt. Express 24(2), 1587–1597 (2016).
[Crossref] [PubMed]

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

L. Yuan, L. Zhou, and W. Jin, “Quasi-distributed strain sensing with white-light interferometry: a novel approach,” Opt. Lett. 25(15), 1074–1076 (2000).
[Crossref] [PubMed]

Yuan, Y.

Z. Yu, J. Yang, Y. Yuan, C. Li, S. Liang, L. Hou, F. Peng, B. Wu, J. Zhang, Z. Liu, and L. Yuan, “Quasi-distributed birefringence dispersion measurement for polarization maintain device with high accuracy based on white light interferometry,” Opt. Express 24(2), 1587–1597 (2016).
[Crossref] [PubMed]

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Yukimatsu, K.

K. Takada, A. Himeno, and K. Yukimatsu, “Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry,” Appl. Phys. Lett. 59(20), 2483–2485 (1991).
[Crossref]

Zhang, H.

Zhang, J.

Zhang, Y.

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

H. Zhang, W. Ye, D. Jia, and Y. Zhang, “Sensitivity enhancement of distributed polarization coupling detection in Hi-Bi fibers,” Chin. Opt. Lett. 10(4), 040603 (2012).
[Crossref]

W. Jing, Y. Zhang, G. Zhou, H. Zhang, Z. Li, and X. Man, “Rotation angle optimization of the polarization eigenmodes for detection of weak mode coupling in birefringent waveguides,” Opt. Express 10(18), 972–977 (2002).
[Crossref] [PubMed]

Zhang, Z.

Zhou, A.

C. Li, J. Yang, Y. Yuan, A. Zhou, D. Yan, J. Chai, S. Liang, L. Hou, B. Wu, F. Peng, Y. Zhang, Z. Liu, and L. Yuan, “A differential delay line for optical coherence domain polarimetry,” Meas. Sci. Technol. 26(4), 045102 (2015).
[Crossref]

J. Yang, Y. Yuan, A. Zhou, J. Cai, C. Li, D. Yan, S. Huang, F. Peng, B. Wu, Y. Zhang, Z. Liu, and L. Yuan, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014).
[Crossref]

Zhou, G.

Zhou, L.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

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[Crossref]

Opt. Lett. (4)

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Figures (7)

Fig. 1
Fig. 1 Traditional PMC measurement schematic based on WLI. (SLD: light-emitting diode, MZI: Mach-Zehnder interferometer, DUT: device under test, C: coupler, M: motor, SPU: signal processor unit, PD: photodiode, and DAQ: data acquisition.)
Fig. 2
Fig. 2 PBS-calibrated system used to observe PMC utilizing WLI. (DFB: distributed feedback laser, WDM: wavelength division multiplex, PBS: polarization beam splitter, and other abbreviations are listed in Fig. 1)
Fig. 3
Fig. 3 Experiment results of a PMF with angle combination (a) 0°–45°, (b) 0°–0°, and (c) 0°–90°. The main interferogram P 0 (12.7 dB) only exists in Fig. (a). Interferograms P (−18.6 dB), P (−12.0 dB) and P (−12.2 dB) marked with red circles—as a remarkable interferogram for calibrating—represent the same coupling point introduced by the same system polarizer. Besides, the noise floors of different angle combinations are labeled by red lines.
Fig. 4
Fig. 4 The dynamic ranges versus detector light intensity. The theoretical results influenced by different noises are illustrated as follows: (a) blue line—only by σ shot 2 , (b) red line—only by σ beat 2 , (c) green line—only by σ circuit 2 , and (d) black line—by the total noise σ i 2 . Some parameters are adopted that R e f f = 100 k Ω , B = 1.2k Hz and R = 0.65 A / W . The experimental results with angle combination 0°–45° are marked with black points. Moreover, the experimental dynamic range calibrated by angle combinations 0°–0° and 0°–90° are marked with dark blue and light blue points, respectively.
Fig. 5
Fig. 5 The connection configuration for testing Y-junction utilizing PBS-calibrated system. The system polarizer (45°-rotated) is spliced to the input pigtail of Y-junction with 0° (at point A). The output pigtail of Y-junction is aligned to the input pigtail of PBS by a fiber fusion splicer (at point O).
Fig. 6
Fig. 6 Intensity distribution yielded by interferograms for evaluating a Y-junction with the detection light power of 35 μw. In comparison to the traditional method with angle combination 0°–45° (blue line), two results utilizing PBS-calibrated method with angle combinations (a) 0°–0° and (b) 0°–90° are illustrated denoted by red lines, respectively. The interferograms A, B, C (or C ), and O (or O ) are induced by the coupling points A, B, C and O shown in Fig. 5, respectively. The chip PER of Y-junction leads to the interferograms ε and ε . Other interferograms B 1 , B 2 and A 2 are the 2nd-order coupling. Here, interferogram introduced by coupling point C could be set as the remarkable interferogram for calibrating and interferogram represented the chip PER of Y-junction are to evaluate.
Fig. 7
Fig. 7 Results of 20-times repeated measurement of Y-junction with different angle combinations are marked by (a) black line 0°–45°,(b) blue line 0°–0°, and (c) red line 0°–90°, respectively.

Equations (13)

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{ σ s h o t 2 = 2 e R P d c B σ b e a t 2 = 2 ( 1 + V 2 ) R P s c a n R P r e f B / Δ ν σ c i r c u i t 2 = 4 K T B / R e f f ,
{ P s c a n = P t + P c P r e f = P t + P c ,
{ P d c = P s c a n + P r e f 2 P t P 0 2 P t P t cos ( k 0 Δ l ) P s i g n a l = 2 P t P c cos ( k 0 Δ l ) ,
σ i 2 = 2 ( σ s h o t 2 + σ b e a t 2 + σ c i r c u i t 2 ) = 8 e R P t B + 8 R 2 P t 2 B / Δ ν + 8 K T B / R e f f .
I 0 2 = ( 2 R P 0 ) 2 8 R 2 P t 2 ,
I s i g n a l 2 = ( 2 R P s i g n a l ) 2 = 8 ρ R 2 P t 2 ,
D R 0 = I 0 2 σ i 2 = 1 e B / ( R P t ) + B / Δ ν + K T B / ( R e f f R 2 P t 2 ) .
{ P s c a n 2 P t P r e f 2 P c .
I s i g n a l _ P B S 2 = ( 2 R P s i g n a l _ P B S ) 2 = 32 ρ R 2 P t 2 .
σ i _ P B S 2 = 2 ( σ s h o t 2 + σ b e a t 2 + σ c i r c u i t 2 ) = 8 e P t R B + 32 ρ R 2 P t 2 B / Δ ν + 8 K T B / R e f f .
D R P B S = I 0 2 σ i _ P B S 2 I s i g n a l _ P B S 2 I s i g n a l 2 = 4 e B / ( R P t ) + 4 ρ B / Δ ν + K T B / ( R e f f R 2 P t 2 ) .
Δ l ε = Δ n PMF ( L I A + L A B + L B C ) + Δ n chip L chip ,
{ P E R ( ε ) = P E R ( ε ¯ ) ± Δ ε = 80.0 ± 0.8 dB P E R ( ε ) = P E R ( ε ¯ ) ± Δ ε = 79.5 ± 0.9 dB .

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